Question

A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 8 insects is exposed to the insecticide in a particular experiment. What is the probability that exactly one insect will survive?

Answer 1

Answer:

19.77% probability that exactly one insect will survive

Step-by-step explanation:

For each insect, there are only two possible outcomes. Either they survive, or they do not. The probability of an insect surviving is independent of other insects. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A certain insecticide kills 70% of all insects in laboratory experiments

So 100 - 70 = 30% survive, which means that $p = 0.3$

A sample of 8 insects is exposed to the insecticide in a particular experiment.

This means that $n = 8$

What is the probability that exactly one insect will survive?

This is P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{8,1}.(0.3)^{1}.(0.7)^{7} = 0.1977$

19.77% probability that exactly one insect will survive